Question: Solve for $x$, $ -\dfrac{8}{x - 5} = -\dfrac{x - 2}{4x - 20} + \dfrac{10}{x - 5} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $x - 5$ $4x - 20$ and $x - 5$ The common denominator is $4x - 20$ To get $4x - 20$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ -\dfrac{8}{x - 5} \times \dfrac{4}{4} = -\dfrac{32}{4x - 20} $ The denominator of the second term is already $4x - 20$ , so we don't need to change it. To get $4x - 20$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{10}{x - 5} \times \dfrac{4}{4} = \dfrac{40}{4x - 20} $ This give us: $ -\dfrac{32}{4x - 20} = -\dfrac{x - 2}{4x - 20} + \dfrac{40}{4x - 20} $ If we multiply both sides of the equation by $4x - 20$ , we get: $ -32 = -x + 2 + 40$ $ -32 = -x + 42$ $ -74 = -x $ $ x = 74$